CN106211149A - Channel reciprocity enhancement method based on principal component analysis - Google Patents
Channel reciprocity enhancement method based on principal component analysis Download PDFInfo
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Abstract
The invention discloses a kind of channel reciprocity Enhancement Method based on principal component analysis, first the measured value of upstream and downstream channel feature is gathered respectively by radio communication both sides Alice Yu Bob, then the upstream and downstream channel characteristic measurements collected is carried out sample packet division respectively, obtain channel characteristics sample group, side wireless communication Alice and Bob carries out principal component analysis process to each described channel characteristics sample group again, finally gives the result with high reciprocity.The present invention solves the channel characteristics measured value reciprocity reduction caused by measurement noise and environment noise and the wireless channel caused by height correlation between measured value generates the problem that key randomness is inadequate.The present invention, for strengthening the safety of wireless communication system, can be applied particularly to the field such as secure communication, military communication, can be extended to multi-node communication scene.
Description
Technical field
The invention belongs to field of communication security, relate to the key generation techniques in wireless communication system.
Background technology
Along with the development of science and technology, Wireless Telecom Equipment sharply increases, and the opening of wireless transmission medium, wireless terminal
The unstability of mobility and network structure also makes the reliability of transmission and security facing acid test.Conventional security
Scheme is to be encrypted data by public and private key in Internet, and private key encryption faces the problem of key management and distribution,
And the complexity of public key encryption is too high.But the LTE/LTE-Advanced currently promoted the use of is even the most perfect
In 5th third-generation mobile communication standard, encryption and decryption real-time, complexity and time delay etc. are proposed more by high message transmission rate
Strict requirements.It addition, be obtained in military and civilian at present at wireless sensor network and wireless self-organization network etc.
In the new network used widely, node is generally powered with battery, it is impossible to bears the power of traditional enciphering and deciphering algorithm and becomes
This expense.At short notice it cannot be cracked additionally, traditional AES is mostly based on existing computer.With
The appearance having the quantum computer performing rapidly the complicated Factorization ability of flood tide, the most traditional encryption method will not
The most reliable.
Meanwhile, the safety of physical layer side of the transmission characteristics such as the multipath of wireless channel, reciprocity, space uniqueness is utilized
Case has obtained extensive concern both domestic and external.According to the reciprocity of wireless channel, communicating pair same time same frequency sends
Signal is by fading characteristic identical for experience.In tdd systems, if the pilot tone of communicating pair sends time difference less than phase
The dry time, bipartite channel height correlation, and the third party's observation outside any one distance communication both sides' half wavelength
The channel arrived is all extremely low with this channel relevancy.Thus, communicating pair utilizes the wireless channel in above tdd systems special
Property generate key as natural stochastic source, solve encryption key distribution and the problem of difficult management of tradition private key encryption.
In recent years, except theory analysis, under tdd systems, the experimental analysis of wireless channel key generation scheme also obtained
To development, analysis result is pointed out in systems in practice, is affected by factors such as time difference, hardware fingerprint and measurement noises, logical
The cipher consistency that letter both sides generate is poor；Additionally, in multicarrier and multiaerial system, the frequency of channel observation, space
Autocorrelation coefficient with time domain is higher, causes the randomness generating key relatively low.These problems will badly influence wireless communication
Road key generates the actual application of scheme.
Summary of the invention
Technical problem: the present invention provides a kind of communicating pair that improves under tdd systems to generate the concordance of key,
The autocorrelation of time domain, frequency domain and spatial domain between removal measured value, improves and produces dividing based on main constituent of key randomness
The channel reciprocity Enhancement Method of analysis.
Technical scheme: the channel reciprocity Enhancement Method based on principal component analysis of the present invention, first double by radio communication
Side Alice Yu Bob gathers the measured value of upstream and downstream channel feature respectively, then special to the upstream and downstream channel collected
Levying measured value and carry out sample packet division respectively, obtain channel characteristics sample group, side wireless communication Alice and Bob is again to each
Described channel characteristics sample group carries out principal component analysis process, finally gives the result with high reciprocity；
Wherein, the method processed the principal component analysis of each channel characteristics sample group comprises the following steps:
1) side wireless communication Alice and side wireless communication Bob obtain respectively the eigenvalue matrix of channel characteristics sample group with
Eigenvectors matrix；
2) respective eigenvalue matrix and eigenvectors matrix are ranked up by Alice with Bob respectively, the spy after sequence
Levy vector matrix and intercept column vector, form respective principal component transform matrix；
3) Alice Yu Bob is respectively by respective current channel characteristics sample group and its principal component transform matrix multiple, obtains
Principal component signal matrix after conversion；
4) Alice Yu Bob is respectively using described for each leisure step 3) in produce principal component signal matrix as present channel
The principal component analysis result output of feature samples group.
In the preferred version of the inventive method, described upstream and downstream channel is characterized as that Alice with Bob is believed by pilot tone
Number calculated received signal strength, channel magnitude, phase place or channel condition information feature；In multi-carrier systems, described
Channel characteristics includes the channel information of time domain and frequency domain；In multi-antenna systems, described channel characteristics includes time domain and spatial domain
Channel information.
In the preferred version of the inventive method, the sample packet division methods of described channel characteristics measured value is as follows:
First channel characteristics measured value is divided into multiple channel characteristics sample by coherence bandwidth, correlated antenna and coherence time
This: have the channel characteristics measured value of same coherent bandwidth, correlated antenna and parameter area coherence time by frequency, antenna, time
Between order composition one column vector, using a column vector as a channel characteristics sample, channel in each channel characteristics sample
The number of characteristic measurements is as the length of this sample；
Then by all channel characteristics samples by frequency, antenna, time sequencing composition channel characteristics sample group, described channel
In feature samples group, the number of sample is more than or equal to the length of sample.
In the preferred version of the inventive method, described step 1) in, Alice Yu Bob is by appointing in following three kinds of methods
A kind of eigenvalue matrix and eigenvectors matrix of obtaining:
One, Alice Yu Bob calculates the covariance matrix of respective channel characteristics sample group respectively, and respectively to each
Covariance matrix carry out Eigenvalues Decomposition or singular value decomposition, it is thus achieved that respective eigenvalue matrix and eigenvectors matrix；
Its two, first the side that communicates calculates the covariance matrix of its channel characteristics sample group, then by this covariance matrix
Be sent to the opposing party that communicates, described communication the opposing party using the covariance matrix that receives as oneself covariance matrix, then
Communicating pair carries out Eigenvalues Decomposition or singular value decomposition to respective covariance matrix respectively, it is thus achieved that respective eigenvalue square
Battle array and eigenvectors matrix；
Its three, first the side that communicates calculates the covariance matrix of its channel characteristics sample group, enters described covariance matrix
Row Eigenvalues Decomposition or singular value decomposition, it is thus achieved that its eigenvalue matrix and eigenvectors matrix, then by this feature value matrix
Be sent to the opposing party that communicates with eigenvectors matrix, described communication the opposing party is by the eigenvalue matrix received and characteristic vector square
Battle array is as oneself eigenvalue matrix and eigenvectors matrix.
In the preferred version of the inventive method, described step 2) in, eigenvalue matrix and the sequence side of eigenvectors matrix
Method is: by eigenvalue matrix according to eigenvalue from big to small order arrangement, according to this sequence, synchronization control eigenvectors matrix
In with the order of the characteristic vector one to one of eigenvalue in eigenvalue matrix, described eigenvalue is characterized diagonal in value matrix
On element, the column vector that described character vector is characterized in vector matrix.
In the preferred version of the inventive method, described step 2) in, according to following either method feature after sequence to
Moment matrix intercepting column vector:
One, intercepts main constituent signal to noise ratio in eigenvectors matrix and is more than or equal to the row of user-defined snr threshold
Vector, described main constituent signal to noise ratio is each characteristic vector characteristic of correspondence value in principal component transform matrix and noise variance
Ratio；
Its two, in the eigenvectors matrix after sequence intercept before several column vectors, intercepting column vector number by
Alice with Bob arranges in advance according to channel condition.
The present invention is applicable to multiaerial system and broadband wireless system, utilize principal component analysis remove channel characteristics signal it
Between the dependency of time domain, frequency domain and spatial domain, to strengthen the randomness generating key；Additionally, due to main composition
The least by effect of noise, by eigenvalue being sorted from big to small and only selecting front portion to have high main constituent signal to noise ratio
Characteristic vector constitute principal component transform matrix, the method be effectively improved communicating pair generate key concordance.
Beneficial effect: compared with prior art, the invention have the advantages that
Signal after quantifying is used length 1 and length 0 detection to reduce long 1 with long 0 probability occurred to increase by existing technology
The randomness of strong encryption keys, but this method can only the identical bit of removal regular length of machinery, can not effectively improve close
The randomness of key.Existing technology amplifies also by privacy that the bit stream after key agreement carries out Hash mapping is close to strengthen
The randomness of key, if but needing the quantity of information that the bit stream randomness difference carrying out key agreement will cause syndrome to be revealed more
Greatly, the safe key after removing syndrome length remains little.If additionally, the randomness of signal before privacy is amplified is the most weak,
Listener-in can be by method breaking cryptographic keys such as dictionary attacks.The present invention proposes the method utilizing principal component analysis, removes and surveys
The dependency of time domain, frequency domain and spatial domain between amount sample, eliminates data redundancy, improves system effectiveness.
Measured value is projected on mutually orthogonal each composition by the present invention by principal component analysis, and measures noise and environment
The impact of the main constituent that noise is big on eigenvalue is much smaller than the composition little to eigenvalue.Accordingly, little by discard portion eigenvalue
Composition, and only utilize the significant main constituent of eigenvalue generate key be effectively improved channel characteristics after principal component analysis
Reciprocity, thus improve generate wireless channel key concordance.
Three kinds of eigenvalue matrix of the present invention are with eigenvectors matrix method, and under first method, Alice and Bob does not has
Transmitting any information, listener-in cannot obtain principal component signal matrix, and safety is protected；In second and the third method
Deliver covariance matrix and eigenvalue matrix, eigenvectors matrix respectively, and owing to these matrixes only represent part system
Meter information, is optionally located in what channel characteristics measured value that the listener-in outside coherence distance collects and Alice and Bob collected
Channel characteristics measured value is the most uncorrelated, so listener-in cannot steal principal component signal matrix effectively, safety is protected.
The channel reciprocity Enhancement Method based on principal component analysis that the present invention proposes, may extend to general communication system
System.
Accompanying drawing explanation
Fig. 1 is the system block diagram in the inventive method；
Fig. 2 is that the eigenvalue matrix in the inventive method generates method one with eigenvectors matrix；
Fig. 3 is that the eigenvalue matrix in the inventive method generates method two with eigenvectors matrix；
Fig. 4 is that the eigenvalue matrix in the inventive method generates method three with eigenvectors matrix.
Detailed description of the invention
Below in conjunction with embodiment and Figure of description, the present invention is described in further detail.
In the embodiment of the inventive method, channel reciprocity Enhancement Method based on principal component analysis provides a kind of in the time-division
Strengthen the reciprocity of channel characteristics under duplex system, remove dependency between channel characteristics sample, improve communicating pair and generate key
Concordance, improve produce key randomness realization means.
Definition Alice and Bob is communicating pair.The channel characteristics of definition Alice to Bob is HAB, the letter of Bob to Alice
Road is characterized as HBA, HABAnd HBAIt is time, frequency, space three-dimensional channel matrix.WithIt is respectively Alice and Bob to pass through
The method calculated channel characteristics measured values such as channel estimation,WithIt is time, frequency, space three-dimensional matrix.
The preprocessing process of the channel characteristics after the present embodiment descriptive system radio channel characteristic information gathering, system is wide
Broadcast, synchronize, Stochastic accessing, the key such as link and follow-up quantization, information mediation, privacy amplification such as sampling generate link and do not exist
This embodiment is described.In the present embodiment, Alice and Bob is respectively provided with stronger computing capability, leading between similar base station
Letter scene.In the present embodiment, Alice and Bob has strict security requirement, in order to avoid key information is let out to the key generated
Dew, in the present embodiment, Alice and Bob does not has any information to hand in channel reciprocity Enhancement Method based on principal component analysis
Mutually.
The flow chart of data processing of Alice and Bob described separately below.
The system block diagram of the present invention as it is shown in figure 1, the generation method of wireless key is divided into channel characteristics sample packet to divide,
Principal component transform matrix calculus and three key links of principal component signal matrix calculus.
1. channel characteristics sample packet division link process step is as follows:
1) Alice and Bob respectively willWithIn there is same coherent bandwidth, correlated antenna and parameter coherence time
The channel characteristics measured value of scope is by frequency, antenna, time sequencing composition column vector xA iAnd xB i, define xA iAnd xB iSpecial for channel
Levy sample, xA iAnd xB iDimension M as the length of sample.
2) each sample described is formed channel characteristics sample group by frequency, antenna, time sequencing by Alice and Bob respectivelyWithWherein N >=M.
2. principal component transform matrix calculus link process step is as follows:
1) Alice and Bob calculates X respectively as shown in Figure 2AAnd XBCovariance matrix
2) Alice and Bob is respectively to covariance matrix RAAnd RBCarry out Eigenvalues Decomposition, Wherein diagonal matrix ΛAAnd ΛBRepresentative feature value matrix, unitary matrice UAAnd UBRepresent characteristic of correspondence moment of a vector
Battle array.
3) Alice and Bob is to ΛAAnd ΛBIn eigenvalue sort from big to small, simultaneously adjust eigenvectors matrix UAWith
UBOrder.Eigenvalue matrix after sequence isWithAccordingly, the eigenvectors matrix after sequence
WithWhereinFor with eigenvalueCharacteristic of correspondence vector,For corresponding special
Value indicativeCharacteristic vector.Each main constituent signal to noise ratio of definition Alice and Bob is respectively each characteristic vector characteristic of correspondence
Value and noise variance σnRatio, i.e.
4) according to the bit error rate requirement of user, corresponding signal to noise ratio demand threshold is inquired by system emulation empirical table
ηthr, Alice and Bob chooses satisfied respectivelyWithCharacteristic vector constitute principal component transform matrixWithWherein K is the individual of the characteristic vector more than or equal to signal to noise ratio demand threshold
Number.
3. principal component signal matrix calculus link process step is as follows:
1) Alice and Bob is respectively by principal component transform matrix U 'AWith U 'BWith former channel characteristics signal XAAnd XBBe multiplied composition
Principal component signal matrix after conversionWithAs follows
2) the principal component signal matrix Y that Alice Yu Bob will produceAAnd YBMain constituent as current channel characteristics sample group
Analysis processing result exports.
Embodiment 2:
It is respectively provided with stronger computing capability for applying the present invention to Alice and Bob in communication system, Alice and Bob pair
The key generated have a highest conformance requirement, and allow Alice and Bob to have under the mutual scene of a small amount of information, make
On the basis of the processing links basically identical with the detailed description of the invention 1 of the inventive method, channel characteristics sample packet divides
Identical with principal component signal matrix calculus link, and principal component transform matrix calculus is modified as follows:
1. principal component transform matrix calculus link process step is as follows:
1) Alice calculates X as shown in Figure 3ACovariance matrix
2) Alice is by covariance matrix RAPass to Bob, Bob and receive the covariance matrix association side as oneself of Alice
Difference matrix RB=RA。
3) Alice and Bob is respectively to covariance matrix RAAnd RBCarry out Eigenvalues Decomposition,
Wherein diagonal matrix ΛA=ΛBRepresentative feature value matrix, unitary matrice UA=UBRepresent characteristic of correspondence vector matrix.
4) Alice and Bob is to ΛAAnd ΛBIn eigenvalue sort from big to small, simultaneously adjust eigenvectors matrix UAWith
UBOrder.Eigenvalue matrix after sequence isWithAccordingly, the eigenvectors matrix after sequence
WithWhereinFor character pair valueCharacteristic vector,For character pair
ValueCharacteristic vector.Definition Alice and Bob each main constituent signal to noise ratio be respectively each characteristic vector characteristic of correspondence value with
Noise variance σnRatio, i.e.
4) according to the bit error rate requirement of user, corresponding signal to noise ratio demand threshold is inquired by system emulation empirical table
ηthr, Alice and Bob chooses satisfied respectivelyWithCharacteristic vector constitute principal component transform matrixWithWherein K is the individual of the characteristic vector more than or equal to signal to noise ratio demand threshold
Number.
Embodiment 3:
For applying the present invention to Alice in communication system, there is stronger computing capability, and the computing capability of Bob is relatively
Weak, it is allowed to Alice and Bob has under the scene that a small amount of information is mutual, using detailed description of the invention 1 base with the inventive method
On the basis of this consistent processing links, channel characteristics sample packet divides identical with principal component signal matrix calculus link, and
Principal component transform matrix calculus is modified as follows:
1. principal component transform matrix calculus link process step is as follows:
1) Alice calculates X as shown in Figure 4ACovariance matrix
2) Alice is to covariance matrix RACarry out Eigenvalues Decomposition,Wherein diagonal matrix ΛARepresent spy
Value indicative matrix, unitary matrice UARepresent characteristic of correspondence vector matrix.
3) Alice is by eigenvalue matrix ΛAWith eigenvectors matrix UAPass the eigenvalue matrix that Bob, Bob receive Alice
With eigenvectors matrix as oneself eigenvalue matrix and eigenvectors matrix ΛB=ΛA, UB=UA。
4) Alice and Bob is to ΛAAnd ΛBIn eigenvalue sort from big to small, simultaneously adjust eigenvectors matrix UAWith
UBOrder.Eigenvalue matrix after sequence isWithAccordingly, the eigenvectors matrix after sequence
WithWhereinFor character pair valueCharacteristic vector,For character pair
ValueCharacteristic vector.Each main constituent signal to noise ratio of definition Alice and Bob is respectively each characteristic vector characteristic of correspondence value
With noise variance σnRatio, i.e.
4) according to the bit error rate requirement of user, corresponding signal to noise ratio demand threshold is inquired by system emulation empirical table
ηthr, Alice and Bob chooses satisfied respectivelyWithAll characteristic vectors constitute principal component transform matrixWithWherein K is the individual of the characteristic vector more than or equal to signal to noise ratio demand threshold
Number.
Above-described embodiment is only the preferred embodiment of the present invention, it should be pointed out that: for the ordinary skill of the art
For personnel, under the premise without departing from the principles of the invention, it is also possible to making some improvement and equivalent, these are to the present invention
Claim improve with equivalent after technical scheme, each fall within protection scope of the present invention.
Claims (6)
1. a channel reciprocity Enhancement Method based on principal component analysis, it is characterised in that in the method, first by channel radio
Letter both sides Alice Yu Bob gathers the measured value of upstream and downstream channel feature respectively, then to the up and descending letter collected
Road characteristic measurements carries out sample packet division respectively, obtains channel characteristics sample group, and side wireless communication Alice and Bob is the most right
Each described channel characteristics sample group carries out principal component analysis process, finally gives the result with high reciprocity；
Wherein, the method processed the principal component analysis of each channel characteristics sample group comprises the following steps:
1) side wireless communication Alice and side wireless communication Bob obtains eigenvalue matrix and the feature of channel characteristics sample group respectively
Vector matrix；
2) respective eigenvalue matrix and eigenvectors matrix are ranked up by Alice with Bob respectively, from sequence after feature to
Moment matrix intercepts column vector, forms respective principal component transform matrix；
3) Alice Yu Bob is respectively by respective current channel characteristics sample group and its principal component transform matrix multiple, is converted
After principal component signal matrix；
4) Alice Yu Bob is respectively using described for each leisure step 3) in produce principal component signal matrix as current channel characteristics
The principal component analysis result output of sample group.
Channel reciprocity Enhancement Method based on principal component analysis the most according to claim 1, it is characterised in that described
Upstream and downstream channel is characterized as that Alice with Bob is by the calculated received signal strength of pilot signal, channel magnitude, phase
Position or channel condition information feature；In multi-carrier systems, described channel characteristics includes the channel information of time domain and frequency domain；Many
In antenna system, described channel characteristics includes the channel information of time domain and spatial domain.
Channel reciprocity Enhancement Method based on principal component analysis the most according to claim 1, it is characterised in that described letter
The sample packet division methods of road characteristic measurements is as follows:
First channel characteristics measured value is divided into multiple channel characteristics sample by coherence bandwidth, correlated antenna and coherence time:
There is the channel characteristics measured value of same coherent bandwidth, correlated antenna and parameter area coherence time suitable by frequency, antenna, time
Sequence one column vector of composition, using a column vector as a channel characteristics sample, channel characteristics in each channel characteristics sample
The number of measured value is as the length of this sample；
Then by all channel characteristics samples by frequency, antenna, time sequencing composition channel characteristics sample group, described channel characteristics
In sample group, the number of sample is more than or equal to the length of sample.
Channel reciprocity Enhancement Method based on principal component analysis the most according to claim 1, it is characterised in that described step
Rapid 1), in, Alice Yu Bob is by any one acquisition eigenvalue matrix and the eigenvectors matrix in following three kinds of methods:
One, Alice Yu Bob calculates the covariance matrix of respective channel characteristics sample group respectively, and respectively to respective association
Variance matrix carries out Eigenvalues Decomposition or singular value decomposition, it is thus achieved that respective eigenvalue matrix and eigenvectors matrix；
Its two, first the side that communicates calculates the covariance matrix of its channel characteristics sample group, is then sent by this covariance matrix
Giving communication the opposing party, the covariance matrix that receives as oneself covariance matrix, is then communicated by described communication the opposing party
Both sides carry out Eigenvalues Decomposition or singular value decomposition to respective covariance matrix respectively, it is thus achieved that respective eigenvalue matrix with
Eigenvectors matrix；
Its three, first the side that communicates calculates the covariance matrix of its channel characteristics sample group, and described covariance matrix is carried out spy
Value indicative is decomposed or singular value decomposition, it is thus achieved that its eigenvalue matrix and eigenvectors matrix, then by this feature value matrix with special
Levying vector matrix and be sent to the opposing party that communicates, the eigenvalue matrix received is made by described communication the opposing party with eigenvectors matrix
Eigenvalue matrix and eigenvectors matrix for oneself.
Channel reciprocity Enhancement Method based on principal component analysis the most according to claim 1, it is characterised in that described step
Rapid 2) in, the sort method of eigenvalue matrix and eigenvectors matrix is: by eigenvalue matrix according to eigenvalue from big to small
Order arrangement, according to this sequence, with the feature one to one of eigenvalue in eigenvalue matrix in synchronization control eigenvectors matrix
The order of vector, described eigenvalue is characterized the element in value matrix on diagonal, and described character vector is characterized vector
Column vector in matrix.
Channel reciprocity Enhancement Method based on principal component analysis the most according to claim 1, it is characterised in that described step
Rapid 2) in, according to following either method eigenvectors matrix intercepting column vector after sequence:
One, intercept main constituent signal to noise ratio in eigenvectors matrix more than or equal to user-defined snr threshold row to
Amount, described main constituent signal to noise ratio is each characteristic vector characteristic of correspondence value in principal component transform matrix and the ratio of noise variance
Value；
Its two, several column vectors before intercepting in the eigenvectors matrix after sequence, intercept the number of column vector by Alice and
Bob arranges in advance according to channel condition.
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| CN107124716A (en) * | 2017-06-05 | 2017-09-01 | 东南大学 | Wireless channel dynamic key production method based on fixed position |
| CN108366370A (en) * | 2018-02-02 | 2018-08-03 | 东南大学 | Quantify the information transferring method of privately owned asymmetric key based on radio channel characteristic |
| CN109618336A (en) * | 2019-01-24 | 2019-04-12 | 东南大学 | A kind of key extraction method in frequency division duplex system |
| CN114531227A (en) * | 2021-12-28 | 2022-05-24 | 华南师范大学 | Wide signal-to-noise ratio continuous variable QKD data coordination method and system based on compression state |
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| KR100681393B1 (en) * | 2006-03-31 | 2007-02-28 | 재단법인서울대학교산학협력재단 | Multipath estimation using channel parameters matrix extension with virtual sensors |
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| Publication number | Priority date | Publication date | Assignee | Title |
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| CN107124716A (en) * | 2017-06-05 | 2017-09-01 | 东南大学 | Wireless channel dynamic key production method based on fixed position |
| CN107124716B (en) * | 2017-06-05 | 2019-07-12 | 东南大学 | Wireless channel dynamic key production method based on fixed position |
| CN108366370A (en) * | 2018-02-02 | 2018-08-03 | 东南大学 | Quantify the information transferring method of privately owned asymmetric key based on radio channel characteristic |
| CN108366370B (en) * | 2018-02-02 | 2019-08-02 | 东南大学 | A kind of information transferring method quantifying privately owned asymmetric key based on radio channel characteristic |
| CN109618336A (en) * | 2019-01-24 | 2019-04-12 | 东南大学 | A kind of key extraction method in frequency division duplex system |
| CN114531227A (en) * | 2021-12-28 | 2022-05-24 | 华南师范大学 | Wide signal-to-noise ratio continuous variable QKD data coordination method and system based on compression state |
| CN114531227B (en) * | 2021-12-28 | 2023-06-30 | 华南师范大学 | Compression-state-based wide signal-to-noise ratio continuous variable QKD data coordination method and system |
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